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When the capacitor with capacitance \(C\) is discharged through a resistor \(R\), starting at the initial voltage \(U_0 \), the voltage \( U_{\text C}(t) \) across the capacitor follows the an exponential curve:\[ U_{\text C}(t) = U_0 \, e^{-\frac{t}{R\,C}} \]
As \(t\) approaches infinity (after waiting for a long time), the voltage \(U_{\text C}(t)\) approaches zero.